Build a Universe with the CMB Power Spectrum Analyzer

Using the faint temperature patterns formed in the sky by cosmic microwaves, scientific analysis can measure things like the age, shape, and composition of the early universe. Looking out at the universe, back in time, we see evolution of matter from hot plasma, to very simple clouds of hydrogen gas, to complex galaxies and planets. The universe can have strange properties, but simple structures like plasma and hydrogen gas behave in predictable ways- for which we can create accurate computer models of behavior.

The Cosmic Microwave Background (CMB) Analyzer shows how the energy signature (called the Angular Power Spectrum) varies as some of the more important input parameters of our universe are modified. The blue line is the CMB power spectrum for "your" universe. Try changing amounts of each ingredient and property. See if you can get the blue line to match the red line, which is based on the measurements from the WMAP mission. The WMAP science team does the same thing, only with high speed super-computers, tens of thousands of combinations, and many more parameters. To learn more about the parameters you are playing with and how they affect power spectrum, check out the WMAP mission pages. Clues to the correct answer can also be found in the News and Technical portions of the WMAP web site.

The Graph

The early structure of the universe as seen in the CMB can be represented by an angular power spectrum, a plot that shows how the temperature pattern in the early universe varies with progressively measuring smaller and smaller patches of the sky. This in turn reveals the amount of energy emitted by different sized "ripples" of sound echoing through the early matter of the universe. The characteristics of these sound waves in turn reveal the nature of the universe through which they travel.

The horizontal axis of the graph is the patch size and decreases from left to right. The vertical axis measures the power of the temperature signal.

• The black points are the processed WMAP observations with error bars showing the uncertainty in each measurement. The uncertainty increases to the right side of the graph because of the finite resolution of WMAP's optic systems; as the patch size decreases, fewer WMAP measurements will fit within the patch, which increases the uncertainty in the measurement.
• The red line shows the best fit model to the WMAP data points.
• The blue line shows your universe simulation based on your value selections. Your mission is to match the red line!
• The light blue band demonstrates the cosmic variance expected for the model; this is a measure of how likely random chance of our positon relative to other matter in the universe is affecting the results.

The Map

These images show a possible variation of temperature across the entire sky given the model inputs selected. Each image is a simulated map of the entire sky computed using the HEALPix synfast application using the power spectra shown in the plots. The map is displayed in a Mollweide projection in Galactic coordinates. Temperature variations are scaled between -0.4 to 0.4 milliKelvin from a mean temperature of 2.73 Kelvin.

Each synfast process used the same random number seed so as to fix the maps' geometry in space; each map will therefore show only the differences in the input parameters to the model. Note that the visible differences between maps is generaly quite small and may not be apparent on this scale. The image matching the model closest to reality will not necessarily look identical to the observed sky because these images are simulated sky maps with similar statistical properties to maps computed from actual data.

The Universe Content: the Ingredients

There are three ingredients in this universe: normal matter (or atoms), cold dark matter, and dark energy.

• Atoms: The amount of ordinary matter (atoms) in your universe, the stuff you see around you: tables, chairs, planets, stars, etc. Expressed as a percentage of the "critical density".
• Cold Dark Matter: The amount of cold dark matter in your universe, as a percentage of the critical density. Cold dark matter can not be seen or felt, and has not been detected in the laboratory, but it does exert a gravitational pull.
• Dark energy: The amount of dark energy in your universe, as a percentage of the "critical density". Unlike dark matter, dark energy exerts gravitational push (a form of anti-gravity) that is causing the expansion of the universe to accelerate or speed up.

Note that the three ingredients can add up to more than or less than 100%. The sum is compared to a quantity that determines the Flatness of the universe. A "flat" universe is said to be at "critical density", having 100% of the matter and energy needed to be "flat". Euclidean geometry describes a flat universe, but non-Euclidean geometries are needed for the alternatives. If the ingredients add up to more than 100%, then the universe has positive curvature and said to be "closed". This means that it curves around on itself (like the surface of a ball), and that if you go in one direction long enough, you'll get back to where you started. If the ingredients add up to less than 100%, then the universe has negative curvature and is called "open". This is the type of curvature that you'd find (in 2 dimensions) on the surface of a horse's saddle, or a potato chip. In that case, space is curved, but it doesn't wrap back around on itself. (Footnote: Mathematicians can probably come up with pathological models where positively curved universes don't wrap around on themselves, and negatively curved ones do, by cutting and pasting various parts of the universe together. We just describe the simplest cases here.)

The Age of the universe is controlled by the amount of the ingredients and the flatness of the universe. By viewing the scale of the universe now, and using Einstein's General Relativity equations to compute the time, under these conditions, needed to reverse the universe to "zero" size, we have the age calculated for us.

Other Properties

The three additional properties of the universe that you can set are the Hubble constant, the reionization redshift, and the spectral index.

• Hubble Constant: indicates how fast the universe is currently expanding (in units of kilometers per second per Megaparsec). It is a measure of how fast an object is moving away from us based upon its distance from the Earth today.
• Reionization Redshift: The era when the first stars formed, expressed in redshift units. The radiation produced by the first stars stripped electrons off hydrogen atoms in the surrounding gas. Some of these electrons scatter CMB photons, changing the properties of the CMB fluctuations. Redshift is a common measure of how much the universe has expanded since a given era: e.g., a redshift of 1 is the era when the universe was ¹/₂ its present size (and roughly half its present age), while a redshift of 10 is when the universe was ¹/₁₁ its present size, and so forth.
• Spectral Index: describes the initial density ripples in the universe. A smaller spectral index means the ripples with longer wavelengths are stronger, and with shorter wavelengths weaker. This has the effect of raising the CMB power spectrum on one side and lowering it on the other. The Spectral Index is like a fingerprint of the very beginning of the universe in that first trillionth of a second after the Big Bang called Inflation. How matter was distributed during that initial expansion will give us clues to the nature of the energy field controlling the inflation.

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